Hepaly · Free Tool
Logic sequences of patterns and numbers, complete with underlying rules.
Select a difficulty level, from simple shape patterns for younger children to challenging number sequences, and generate a printable activity sheet. For every sequence, the generator ensures no alternative simple rule creates a conflicting answer, then supplies the answer key and rule explanation.
- Free, no account needed
- Calculated on your device
- No user input is ever sent
Your sequence worksheet
Pick a level, number of sequences, and a seed: your sheet and answer key are ready.
What are the next two boxes?
View answer key and rules
Answer key
6 patterns; for each one, no other simple rule (constant step, multiplication, alternation, growing step, sum of the two previous, squares, repeated pattern) produces a different sequence.
How to use it
- Choose the level: 1 for shape patterns, 2 for simple addition and subtraction, 3 and 4 for doubling, growing gaps, squares, or sums.
- Enter the number of patterns, then keep the seed or change it for a new worksheet.
- Print the worksheet and keep the answer key separate. Under "View answer key", the rule for each pattern is explained.
- The CSV lists the given terms, answers, and rules to help you prepare a lesson.
A worked example
Example (Level 3): 2, 4, 8, 16, 32, then ? ? The rule is "double the number". Answers: 64 and 128.
Another example: 1, 2, 4, 7, 11: the gaps are 1, 2, 3, 4, so the pattern continues with 16 then 22. The program checks that these terms are not compatible with any other simple rule that would produce different answers.
Method, underlying assumptions, and limits
How it works. Each pattern is generated by a rule (constant addition, subtraction, alternating additions, doubling, tripling, growing gap, sum of the two previous terms, consecutive squares, or a repeated shape pattern). Before keeping it, the program tests these families of rules on the five shown terms: the pattern is only accepted if every compatible rule produces the exact same two answers. Numbers remain under 1,000.
Limitations. A pattern can always be continued using a custom, made-up rule; our verification only covers the rule families listed here, which match elementary school curricula. The levels are general benchmarks: a child might succeed at a higher level or simply need a break.
Frequently asked questions
How do you know there is only one possible answer?
For each pattern, the program applies several families of rules to the displayed terms. If two rules yield different answers, the pattern is rejected and a new one is created.
Which level should I choose for a 6-year-old?
Level 1 (shapes) or 2 (simple addition). Adjust based on how comfortable your child feels, without any pressure.
Can I regenerate the exact same worksheet later?
Yes: using the same settings and the same seed generates the exact same worksheet.
Is any data saved?
No, nothing is sent or stored: everything is calculated directly in your web browser.